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Collaboration and Multitasking in Networks: Architectures, Bottlenecks and Throughput

Motivated by the trend towards more collaboration in work flows, we study stochastic processing networks where some activities require the simultaneous collaboration of multiple human resources. Collaboration introduces resource synchronization requirements that are not captured in the standard procedure (formalized through a static planning problem) to identify bottlenecks and theoretical capacity. We introduce the notions of collaboration architecture and unavoidable idleness. In general, collaboration architectures may feature unavoidable idleness so that the theoretical capacity exceeds the maximal achievable throughput or actual capacity. This fundamental tradeoff between collaboration and throughput does not disappear in multi-server networks and has important ramifications to service-system staffing. We identify a special class of collaboration architectures that have no unavoidable idleness and present a condition on this architecture that guarantees, regardless of the processing times of the various activities, that the standard bottleneck procedure in fact identifies the actual capacity of the network. In multi-server cases this class of networks guarantees that the theoretical capacity is achievable provided one has the right number of floaters. Finally, we study the subtleties that collaboration introduces to questions of flexibility investment. Unavoidable idleness may limit the ability to materialize the benefits of flexibility. We study the interplay of flexibility and unavoidable idleness and offer remedies derived from collaboration architecture.